Mitt Romney eked out a victory in the Michigan primary on Tuesday night, staving off a challenge from Rick Santorum to sidestep what would have been a stinging defeat in his native state. The former Massachusetts governor also coasted in Arizona’s winner-take-all contest, infusing his flagging campaign with a jolt of momentum as the Republican primary fight gears up for 10 Super Tuesday contests on March 6.

On a night that could have dealt his presidential bid a bruising blow, Romney escaped the embarrassment of failing to carry a state that his advisers cast as a must-win contest. With 90% of Michigan’s precincts reporting, the fragile front runner won 41% of the vote, drawing the decisive margin from Oakland County, the affluent suburban Detroit region where he grew up. Santorum captured 38% of the vote, as Romney held down the former Pennsylvania Senator’s edge in rural areas and the conservative Western Michigan counties that formed his stronghold. Ron Paul finished third with 12%, while Newt Gingrich lagged with 7%.

“What a night!” Romney crowed, exhaling as he stepped to the podium at his victory party in suburban Detroit. “We didn’t win by a lot, but we won by enough, and that’s all that counts.”

According to CNN’s exit polls, Romney patched together an affluent, moderate coalition anchored by seniors, among whom he led Santorum by 17 points, 48% to 31%. He outpaced Santorum in the scramble for college graduates and postgrads and rang up a wide lead among the one-third of the Michigan electorate that reported earning more than $100,000 per year. Romney led Santorum by 6 points among voters who dubbed themselves “moderate or liberal,” and by 18 points among the “somewhat conservative.” Voters who cited the ability to oust Barack Obama as pre-eminent sided with Romney, 61% to 24%.

Santorum won “very conservative” voters 50% to 35%, and white Evangelicals by the same margin. He handily won voters who said religious issues mattered “a great deal” or somewhat and carried strong supporters of the Tea Party and those opposed to abortion. Among voters who said the most important attribute in a candidate was being a “true conservative” or possessing “strong moral character,” he crushed Romney 59% to 17%. He also benefited from an influx of Democratic voters who crossed over in hopes of hampering Romney’s chances.

How many delegates Romney will pick up is not yet clear; Michigan apportions two for the winner of each of the state’s 14 congressional districts, plus two for the statewide winner. But he will pad his lead by winning all 29 delegates from Arizona, where he coasted with 48% of the vote, nearly doubling Santorum’s 26%. With 73% of precincts reporting, Gingrich had grabbed 16% of the vote. Paul trailed with 9%.

For Romney, the margin in Michigan was too close for comfort, putting his campaign on tenterhooks as it squirmed at the prospect of dropping the candidate’s native state. A loss would likely have spurred the party’s high priests to publicize their concerns about Romney’s viability as a standard-bearer. But while a win wards off a looming disaster, it doesn’t dispel the doubts enveloping Romney’s candidacy, from his chilly relationship with social conservatives to the prospect of his negative-ad bombardments turning off independents. Nor is it likely to catalyze a sustained surge.

There’s a week for the winds to shift, but the Super Tuesday forecast is mixed for each of the candidates. Romney will be heavily favored in Massachusetts, Vermont and Virginia, where only he and Paul are on the ballot, thanks to the organizational deficits of their rivals. But polls show Santorum with large leads in Tennessee, Oklahoma and the key bellwether of Ohio. Meanwhile, Gingrich has grabbed a big lead in Georgia, the biggest delegate prize of the night and the state where he served in Congress. A Super Tuesday split would ensure that the bruising Republican nominating fight proceeds indefinitely.

For Romney, this Tuesday’s triumphs marked a moment to savor before gearing up for the long slog ahead. “Just a week ago, the pundits and the pollsters were ready to count us out,” he said. The underdog credo was a tad disingenuous coming from a candidate who again relied on his superior finances and an aerial assault from his allied super PAC to beat his opponent. The win wasn’t pretty. But on a night when he fended off a strong challenge from Santorum and padded his delegate lead, Romney will certainly take it.